Leading internet companies including Google have written to business secretary Peter Mandelson urging him to change the new digital economy bill to throw out a controversial clause that could give future ministers sweeping powers to change copyright law.

Their letter, sent to coincide with today's second reading of the recently announced bill in the Lords, voices support for parts of the bill and a "shared respect" for copyright. But Google, Facebook, Yahoo and eBay also express "grave concerns" over proposed measures "which risk stifling innovation and damaging the government's vision for a digital Britain."

They highlight elements of Mandelson's bill introduced at the 11th hour: "In particular, we believe the bill's clause 17 – which gives any future secretary of state unprecedented and sweeping powers to amend the Copyright, Designs and Patents Act 1988 – opens the way for arbitrary measures. This power could be used, for example, to introduce additional technical measures or increase monitoring of user data even where no illegal practice has taken place," the letter said.

The internet companies warn that such an unclear copyright backdrop could run counter to former communications minister Stephen Carter's Digital Britain report, which examined ways to ensure the UK remained at the leading edge of the global digital economy.

"This would discourage innovation, impose unnecessary costs, potentially unsettling the careful balance of responsibilities for enabling market change which Lord Carter outlined in the Digital Britain report," the letter said. "This clause is so wide that it could put at risk legitimate consumer use of current technology as well as future developments ... The industry as a whole had hoped that the outcome of Digital Britain would be a clear, workable set of principles by which the industry could operate. On the contrary, clause 17 creates uncertainty for consumers and businesses and puts at risk the UK's leading position in a digital Europe. We urge you to remove clause 17 from the bill."

A spokesman for Mandelson's department sought to reassure the internet companies the government would not abuse any future powers.

"The law must keep pace with technology, so that the government can act if new ways of seriously infringing copyright develop in the future. However, business will not wake up one morning to a world in which government has taken extensive digital powers," he said.

While the digital economy bill was welcomed by many media companies, which feel their copyright on music, film and other content need better protection online, it has also faced a large amount of opposition from internet service providers and consumer groups.